Intermediate Microeconomics
Technology
Technology = firm's options for combining inputs
to obtain output
Focus on only two inputs: labor (L) and capital (K)
Production function = schedule that shows the
highest level of output the firm can produce from
a given combination of inputs
Total product of L and K = the highest total
amount of output the firm can produce given the
amount of inputs
Example: F(K, L) = 3L2 + 5K
Chapter 8
Technology and Production
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Production function
Isoquant map
K
Production function is similar to utility function,
with one major difference: if utility is purely
ordinal (its value doesn't matter in itself), the
value of the production function does matter
Isoquant = curve showing all input combinations
that yield the same level of output (similar
concept to indifference curve)
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Isoquant map = collection of all isoquants
corresponding to a particular production function
F(K, L) = Q3
F(K, L) = Q2
F(K, L) = Q1
L
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Decision-making horizon
Properties of production function
Feasible choices of input combinations could
depend on input types:
fixed factor = its level cannot be changed over the
relevant planning horizon
variable factor = its level can be changed
Marginal physical product
Marginal rate of technological substitution
Returns to scale
Hence, planning horizon for production decisions
is important:
short run = time period over which only one of the
firm's inputs is variable and all other are fixed
long run = time period long enough so that all inputs
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are variable
Marginal physical product
Increasing marginal returns
Marginal physical product = extra amount of
output that can be produced when the firm uses
an additional unit of a specific input, holding the
levels of all other inputs constant
Algebraically: derivative of production function
with respect to that particular input
For example, marginal physical product of labor:
MPP L =
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Q
Production function
F(L, Kf)
MPPL
Q
L
L
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2
Decreasing marginal returns
Constant marginal returns
Q
Q
Production function
F(L, Kf)
Production function
F(L, Kf)
MPPL
MPPL
L
L
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Marginal rate of technical
substitution
Marginal rate of technical
substitution
Marginal rate of technical substitution (MRTS) =
rate at which the available technology allows
the substitution of one factor for another
Algebraically: the negative of the slope of the
isoquant equivalent to the marginal rate of
substitution from utility theory
Marginal rate of technical substitution (MTRS):
In our labor/capital example:
MRTS=
K
L
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increasing = technology such that the marginal
physical product of an input rises as the
amount of that input used increases
constant = technology such that the marginal
physical product of an input remains
unchanged as the amount of that input
increases
decreasing = technology such that the
marginal physical product of an input falls as
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the amount of that input used increases
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Two polar cases
Perfect substitutes
Perfect substitutes = two inputs that have a
constant marginal rate of technical substitution
of one for the other
No factor substitution = inputs that cannot be
substituted for one another in any proportion,
but need to be used together in a constant
proportion
K
Isoquants
L
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The relationship between
MRTS and MPP
No factor substitution
K
Along an isoquant, as the amount of inputs
change by L and K, output remains
unchanged:
MPPL × L + MPPK × K = 0
Isoquants
Hence, MPPL × L = – MPPK × K
This in turn means that:
MRTS=
MPP L
MPP K
L
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Returns to scale
Increasing returns to scale = technology such
that a proportional increase in all input levels
leads to greater than proportionate output
growth
Decreasing returns to scale = technology such
that a proportional increase in all input levels
leads to less than proportionate output growth
Constant returns to scale = technology such
that a proportional increase in all input levels
leads to a proportionate output growth
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